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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Linear ill-posed problems on sets of convex functions on two-dimensional sets

V. Titarenko / A. Yagola

Department of Mathematics, Faculty of Physics, Moscow State University, Vorobyevy Gory, 119992, Moscow, Russia. E-mails: ,

Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 14, Issue 7, Pages 735–750, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939406779801988,

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Linear ill-posed problems written as the operator equation A = on sets of functions z convex on multi-dimensional sets Ω are considered in the paper. A regularizing algorithm zη = R(A h, uδ, η), where ||A hA|| ≤ h, ||uδ|| ≤ δ, η = (h,δ), obtained in the previous papers for line segments is generalized such that the approximate solution zη tends to the exact one uniformly on some subsets of the domain Ω. The algorithms to estimate an error of finite dimensional approximation and to find a lower z l and an upper z u functions that bound all approximation solutions are provided.

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